Active Appearance Models (AAMs) employ a paradigm of inverting a synthesis model of how an object can vary in terms of shape and appearance. As a result, the ability of AAMs to register an unseen object image is intrinsically linked to two factors. First, how well the synthesis model can reconstruct the object image. Second, the degrees of freedom in the model. Fewer degrees of freedom yield a higher likelihood of good fitting performance. In this paper we look at how these seemingly contrasting factors can complement one another for the problem of AAM fitting of an ensemble of images stemming from a constrained set (e.g. an ensemble of face images of the same person).